Question

How to find lim (n =>>infinite) F(n+1)/F(n)
Fn is the nth Fibonacci number

Answer 1

\[\lim_{n \rightarrow \infty} F _{n+1}/F _{n}\]

Answer 2

\(F_{n+1}=F_{n}+F_{n-1} \) divide it by \(F_{n} \) then u have \(\large \frac{F_{n+1}}{F_{n}}=1+\frac{F_{n-1}}{F_{n}} \) when n--->infinty \(\large\frac{F_{n+1}}{F_{n}} =L \) and
\(\large\frac{F_{n-1}}{F_{n}} =1/L \)

Answer 3

now u have \(\large L=1+\frac{1}{L} \)

Answer 4

just notice F(n+1)/F(n) and F(n)/F(n-1) are the same when n aproaches to infinity

Answer 5

ok, i think i got it !! awesome !! thx

Answer 6

yw